Language. Unlimited? Possibly. Perfect? Not Likely.

Three Lefts don’t make a Right, but they do make a Square, and may even be potentially responsible for the genesis of Digitized Circles

Lately I’ve been thinking a lot about little squares.  Little squares are easily constructed using very simple mathematics. If we agree( at least in the alien world of computer innards), that little squares, built by 0 and 1 constructors, are capable of manipulating sensory perception to such an extent that most people don't ever consider basic concepts like "curved is a sequence of straights".  "Arcs" are manifests of carefully arranged straight lines, with enough straight lines, we can create such a density of "straights", that Sensorially, we perceive what appear to be images that look nothing like squares or straight lines.

I’ll go out on a limb here and suggest that in a digital context, proper and perfect geometric circles are impossible to construct.  Further, it seems to follow that the observers degree of sensory conviction regarding the truthfulness  of the Digital Circle of Perfection(DCP) is simply evaluated as an inverse proportion to the distance/magnification from which the observer receives information about the “alleged” circle, before passing it along for cognitive evaluation, where if “well” executed by the digital processor, Sensory perceptions and cognitive perceptions would be in agreement that the “circle looking image is truly a circle”

And if a general consensus is reached across a population that the image presented to them results in an agreement between sensory perceptions and cognitive perceptions, with singular( en masse) conviction  that they are indeed observing a circle.  If we can accept this principle, we are also accepting that “circles are made from squares”.  And to extrapolate on this logical sequence, we should be able to say that the number of straight lines or little squares assembled to create this mass geometric quorum is not infinite( which is not to say that little blocks are infinitely divisible), and things that are not infinite are Finite. Finite things can be measured and counted.

So where I am left to think about this a bit more is:  if a quorum of observers declare an image to be a circle, Do is it not?  Now we see the inevitable divide between empirically constructed and observed “circles” and those that are incapable of manifesting digitally (which is not the same as tangibly).  So at this stage, I think we say things like:

1.      Empirical observation and mass quorum, may or may not be able to take something that isn’t, and convert it to something that is( e.g. Squares to circles)

2.       The imagination of a perfect circle is seemingly possible, but impossible to test.

3.       We can build circle-looking images from a finite number of straight lines( or little boxes)

So if we feel that this logic is sound, at what point during the assemblage of the “straights” can we declare that a circle has just been born, and if we can do that, we should be able to establish an infinitely scalable equation that will always be able to tell us how many “straights” are required to yield a “round”, so does:

                S = straight or otherwise square building material

                N = the number of S’s required to yield a perfect and proper digital circle

                C = Circle

 

So:

                C = N * S

Then:

 1) there is a point in time at which a non-circle transitions into circle status

 

2) There is a calculable and reliable number that can be derived such that this number allocates to the “digital circle builder the exact number of straights needed to construct the perfect round by the he builders.  So if this were true, N number of straights makes a round, and we can always solve for N.

Now raise your hand if you believe in this train of logic…..

Now this post is not about circles, it’s about little squares:  

Language. Unlimited? Possibly. Perfect? Not Likely.

Imagine trying to draw a perfectly smooth circle out of straight lines, or little tiny squares. This is in fact what a computer does. Unsophisticated computers produce circles that have jagged edges, like a saw blade. Very fancy computers seem to produce flawless curves and thus perfect circles. But, zoom in close enough on the edge of that “perfect” circle, and you will find the same saw tooth edging that was readily visible on the unsophisticated computer. We can build incredibly complex, and exceptionally sophisticated computers, with the best of the best mathematical algorithms for producing circles, but, when the disks have stopped spinning, zoom in again on this “Uber Circle” and you will still find that same saw toothed edging.

Why? The computer/display does not have “curve”, “arc”, “bend”, “circle”, etc. as a foundational building “block” within its language. It only has “little squares” within its core vocabulary. To represent anything other than squares, elaborate instructions must be given to the computer, explaining to it how to assemble these little tiny squares such that the result is something that does not look like a square. The simpler the computer, the less complex the instructions it can understand, and the more crude the output (let’s assume “circle) will be. Very sophisticated computers can be given very, very complicated instructions on how to assemble the little squares such that the result looks like a circle. But either way, the Circle is still just a bunch of little squares representing themselves to be a circle, with some computers better able than others to tell the story.

Human language is structurally the same, the key difference being that our vocabulary is not restricted to little squares, but our vocabulary is also not perfectly complete. The fewer the vocabulary blocks we possess, the cruder the story we might tell in relation to the actual event. The more sophisticated we are, and the larger the number of vocabulary blocks we possess, the more refined our story appears. But no matter how smooth the arc of our story, zoom in close enough and you will see the same saw tooth edges that we saw with our circle. Why? We can forever converge on linguistic perfection, but the difference between current state linguistics and perfection is infinitely divisible, and thus perfection is never achievable. Just as a square can never be a circle.

And therefore, while unlimited amounts of other linguistic accessories can be layered on top of our vocabulary building blocks to try and smooth the imperfect edges (tone, cadence, volume, etc.), we can maintain that our language is unlimited, but our communications can never be perfect